Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators

A similarity transformation is constructed through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension, can be mapped identically, to a set of free harmonic oscillators. This equivalence provides a straightforward method to find the complete set of eigenfunctions, the exact constants of motion and a linear $W_{1+\infty}$ algebra associated with this model. It is also demonstrated that a large class of models with long-range interactions, both in one and higher dimensions can be made equivalent to decoupled oscillators.Comment: 9 pages, REVTeX, Completely revised, few new equations and references are adde

Nuclear Alpha-Particle Condensates

The $\alpha$-particle condensate in nuclei is a novel state described by a product state of $\alpha$'s, all with their c.o.m. in the lowest 0S orbit. We demonstrate that a typical $\alpha$-particle condensate is the Hoyle state ($E_{x}=7.65$ MeV, $0^+_2$ state in $^{12}$C), which plays a crucial role for the synthesis of $^{12}$C in the universe. The influence of antisymmentrization in the Hoyle state on the bosonic character of the $\alpha$ particle is discussed in detail. It is shown to be weak. The bosonic aspects in the Hoyle state, therefore, are predominant. It is conjectured that $\alpha$-particle condensate states also exist in heavier $n\alpha$ nuclei, like $^{16}$O, $^{20}$Ne, etc. For instance the $0^+_6$ state of $^{16}$O at $E_{x}=15.1$ MeV is identified from a theoretical analysis as being a strong candidate of a $4\alpha$ condensate. The calculated small width (34 keV) of $0^+_6$, consistent with data, lends credit to the existence of heavier Hoyle-analogue states. In non-self-conjugated nuclei such as $^{11}$B and $^{13}$C, we discuss candidates for the product states of clusters, composed of $\alpha$'s, triton's, and neutrons etc. The relationship of $\alpha$-particle condensation in finite nuclei to quartetting in symmetric nuclear matter is investigated with the help of an in-medium modified four-nucleon equation. A nonlinear order parameter equation for quartet condensation is derived and solved for $\alpha$ particle condensation in infinite nuclear matter. The strong qualitative difference with the pairing case is pointed out.Comment: 71 pages, 41 figures, review article, to be published in "Cluster in Nuclei (Lecture Notes in Physics) - Vol.2 -", ed. by C. Beck, (Springer-Verlag, Berlin, 2011

A Unified Algebraic Approach to Few and Many-Body Correlated Systems

The present article is an extended version of the paper {\it Phys. Rev.} {\bf B 59}, R2490 (1999), where, we have established the equivalence of the Calogero-Sutherland model to decoupled oscillators. Here, we first employ the same approach for finding the eigenstates of a large class of Hamiltonians, dealing with correlated systems. A number of few and many-body interacting models are studied and the relationship between their respective Hilbert spaces, with that of oscillators, is found. This connection is then used to obtain the spectrum generating algebras for these systems and make an algebraic statement about correlated systems. The procedure to generate new solvable interacting models is outlined. We then point out the inadequacies of the present technique and make use of a novel method for solving linear differential equations to diagonalize the Sutherland model and establish a precise connection between this correlated system's wave functions, with those of the free particles on a circle. In the process, we obtain a new expression for the Jack polynomials. In two dimensions, we analyze the Hamiltonian having Laughlin wave function as the ground-state and point out the natural emergence of the underlying linear $W_{1+\infty}$ symmetry in this approach.Comment: 18 pages, Revtex format, To appear in Physical Review

Formation of knots in partially replicated DNA molecules.

Bacterial plasmids with two origins of replication in convergent orientation are frequently knotted in vivo. The knots formed are localised within the newly replicated DNA regions. Here, we analyse DNA knots tied within replication bubbles of such plasmids, and observe that the knots formed show predominantly positive signs of crossings. We propose that helical winding of replication bubbles in vivo leads to topoisomerase-mediated formation of knots on partially replicated DNA molecules

Expression of Arabidopsis APETALA1 in tomato reduces its vegetative cycle without affecting plant production

Important agronomic traits such as fruit quality, harvesting efficiency or production largely depend on flowering time. We have analysed the effect of the overexpression of the Arabidopsis APETALA1 MADS-box gene on vegetative and reproductive growth of tomato. Constitutive expression of APETALA1 in tomato plants has major effects on the length of their growth cycle as well as on their growth habit. Transgenic tomato plants initiated flowering after the production of 6 vegetative nodes as compared to 11 nodes for the wild type plants. Most of tomato 35S:AP1 plants also showed determinate growth habit, similar to the phenotype of self pruning tomato mutants, as well as an initial reduction of their axillary growth. Moreover, development and fertility of flowers were not affected in plants expressing AP1. Consequently, fruit formation in transgenic plants grown under greenhouse conditions occurred normally, which permitted a similar fruit yield compared to control plants. Since traits conferred by AP1 expression are dominant, its expression in tomato breeding lines could provide advantages for the development of new hybrid varieties with shorter generation time, determinate growth, and reduced pruning requirements

Remorins form a novel family of coiled coil-forming oligomeric and filamentous proteins associated with apical, vascular and embryonic tissues in plants.

Remorins form a superfamily of plant-specific plasma membrane/lipid-raft-associated proteins of unknown structure and function. Using specific antibodies, we localized tomato remorin 1 to apical tissues, leaf primordia and vascular traces. The deduced remorin protein sequence contains a predicted coiled coil-domain, suggesting its participation in protein-protein interactions. Circular dichroism revealed that recombinant potato remorin contains an alpha-helical region that forms a functional coiled-coil domain. Electron microscopy of purified preparations of four different recombinant remorins, one from potato, two divergent isologs from tomato, and one from Arabidopsis thaliana , demonstrated that the proteins form highly similar filamentous structures. The diameters of the negatively-stained filaments ranged from 4.6-7.4 nm for potato remorin 1, 4.3-6.2 nm for tomato remorin 1, 5.7-7.5 nm for tomato remorin 2, and 5.7-8.0 nm for Arabidopsis Dbp. Highly polymerized remorin 1 was detected in glutaraldehyde-crosslinked tomato plasma membrane preparations and a population of the protein was immunolocalized in tomato root tips to structures associated with discrete regions of the plasma membrane